Control system and vehicle steering control system

ABSTRACT

A control system calculates inputs to a control target that has m inputs and n outputs (m=n, each of m and n is a natural number that is more than one), while designating a plurality of combinations of the inputs and the outputs. A feedback controller calculates, with respect to each designated combination, a control input to a non-interference controller based on a difference between a target value and a current value of the control quantity to make the current value follow the target value. The non-interference controller executes, with respect to each designated combination, a non-interference control to reduce influence due to mutual interference between n control quantities. This reduces the number of combinations of the inputs and the outputs, the combinations whose mutual interference needs considering; thereby, the non-interference control may be easily achieved.

CROSS REFERENCE TO RELATED APPLICATION

The present application is based on Japanese Patent Application No.2012-174856 filed on Aug. 7, 2012, the disclosure of which isincorporated herein by reference.

TECHNICAL FIELD

The present disclosure relates to a control system which controls acontrol target which outputs more than one control quantity.

BACKGROUND ART

[Patent literature 1] JP 2011-186589 A

A control system is known which uses a control target model to performnon-interference control so as to negate or eliminate mutualinterference caused by a plurality of control quantities outputted by acontrol target (refer to Patent literature 1). Such non-interferencecontrol negates the mutual interference by previously adding a quantityequivalent to the mutual interference to the control quantity.

Generally, a control target model, an input signal, or an output signalmay suffer unintentional disturbance. Therefore, when a control targethas a great number of control quantities of inputs and outputs, to posea great number of combinations of mutual interference, it becomesdifficult to realize non-interference control in calculating a transferfunction etc.

Examples of control systems that pose mutual interference include avehicle steering control system, which operates a plurality of steeringactuators depending on steering wheel manipulation by a driver on avehicle to thereby control actual steering angles of front wheels andrear wheels. To be specific, the actuators include an electric powersteering which assists a steering torque of a steering wheel by adriver; a variable gear transfer steering which flexibly changes aturning angle of a front wheel with respect to a turning angle of thesteering wheel; and an active rear steering wheel which flexibly changesa turning angle of a rear wheel with respect to a turning angle of thesteering wheel.

Operations of the plurality of actuators output several vehicle motionproperties such as a steering angle θs, a yaw angle velocity γ, and alateral acceleration ay. At this time, the plurality of actuatorsoperate cooperatively with a rotational movement axis (yaw axis) aroundthe center gravity of the vehicle, involving mutual interference.Furthermore, the vehicle receives disturbance due to rainstorm, blownfragments, or a road surface reactive force depending on the groundingstate between tires and road surfaces. Such disturbance cannot bedetected or presumed in real time practically by any measure.

Thus, it is not realistic to achieve non-interference control, whichpresumes mutual interference between the vehicle motion properties basedon operations of a plurality of actuators and which adds previously aquantity equivalent to the mutual interference to a control quantity. Tothat end, a person with a skilled technique needs to maketrial-and-error to adjust each of the actuators; this requires a numberof time and man hours. The above situation may arise not only in avehicle steering control system but also in a control system that mayundergo mutual interference between a plurality of outputs of a controltarget.

SUMMARY

It is an object of the present disclosure to provide a non-interferencecontrol in a control system which controls a control target whichoutputs a plurality of control quantities, reducing influence by mutualinterference between outputted control quantities.

To achieve the above object, according to an aspect of the presentdisclosure, a control system is provided to control a control targetthat provides a plurality of n outputs of control quantities based on aplurality of m inputs of operation quantities, wherein m=n and each of mand n is a natural number that is more than one. The control systemincludes a plurality of feedback controllers and a non-interferencecontroller. Each of the plurality of feedback controllers is tocalculate the operation quantity based on a difference between (i) atarget value, which is generated by a target value generator, the targetvalue corresponding to the control quantity, and (ii) a current value ofthe output provided by the control target. The non-interferencecontroller is provided between (i) the plurality of feedback controllersand (ii) the control target; the non-interference controller is toexecute a non-interference control to reduce influence due to mutualinterference between the outputs provided by the control target.Further, combinations of the inputs and the outputs in the controltarget are designated; and the non-interference control by thenon-interference controller and the feedback control by the feedbackcontrollers are executed with respect to each of the designatedcombinations of the inputs and the outputs.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features, and advantages of the presentdisclosure will become more apparent from the following detaileddescription made with reference to the accompanying drawings. In thedrawings:

FIG. 1 is a block diagram of a control system according to an embodimentof the present disclosure;

FIG. 2 is a diagram illustrating a configuration of a vehicle steeringcontrol system according to an embodiment of the present disclosure;

FIG. 3A is a diagram illustrating a comparative model of a conventionalvehicle steering control system;

FIG. 3B is a diagram illustrating a model of the vehicle steeringcontrol system according to the embodiment;

FIG. 4 is a block diagram of the vehicle steering control systemaccording to the embodiment of the present invention;

FIG. 5 is a diagram illustrating a frequency characteristic of an outputof a steering angle θs based on an input of each motor voltage beforeapplying non-interference control;

FIG. 6 is a diagram illustrating a frequency characteristic of an outputof a yaw angle velocity γ based on an input of each motor voltage beforeapplying non-interference control;

FIG. 7 is a diagram illustrating a frequency characteristic of an outputof a lateral acceleration ay based on an input of each motor voltagebefore applying non-interference control;

FIG. 8 is a diagram illustrating a frequency characteristic of an outputof a steering angle θs based on an input of each motor voltage afterapplying non-interference control;

FIG. 9 is a diagram illustrating a frequency characteristic of an outputof a yaw angle velocity γ based on an input of each motor voltage afterapplying non-interference control;

FIG. 10 is a diagram illustrating a frequency characteristic of anoutput of a lateral acceleration ay based on an input of each motorvoltage after applying non-interference control;

FIG. 11 is a diagram illustrating a wave form indicating a target valuefollowing characteristic of a steering angle θs by the non-interferencecontroller;

FIG. 12 is a diagram illustrating a wave form indicating a target valuefollowing characteristic of a yaw angle velocity γ by thenon-interference controller;

FIG. 13 is a diagram illustrating a wave form indicating a target valuefollowing characteristic of a lateral acceleration ay by thenon-interference controller;

FIG. 14 is a block diagram illustrating a vehicle steering controlsystem including a control target having m inputs and n outputs (m<n)according to an embodiment of the present disclosure; and

FIG. 15 is a block diagram illustrating a vehicle steering controlsystem including a control target having m inputs and n outputs (m>n)according to an embodiment of the present disclosure.

DETAILED DESCRIPTION

The following describes embodiments of the present disclosure withreference to drawings.

(Control System)

The following will explain a configuration of a control system 10according to an embodiment of the present disclosure with reference toFIG. 1. The control system 10 according to the embodiment is surroundedby broken-line block in FIG. 1. The control system 10 calculates inputsto a control target 20 having m inputs and n outputs (m=n, m is anatural number that is more than one) based on target values r1, r2, . .. , rm which are generated by m target value generators 121, 122, . . ., 12 m (which are collectively referred to as a target value generator12). In this case, mutual interference arises in between the controlquantities y1, y2, . . . , yn that are n outputs of the control target20. In addition, each combination of (i) an input among the inputs and(ii) an output among the outputs in the control target 20 may bedesignated optional. The control quantity serving as an output of thecontrol target 20 may be any one of physical quantities such astemperature, pressure, and position.

The control system 10 includes a feedback controller 13 and anon-interference controller 14. The feedback controller 13 includes mfeedback controllers 131, 132, . . . , 13 m corresponding to targetvalues r1, r2, . . . , rm. The feedback controller 13 calculates thecontrol inputs v1, v2, . . . , vm to the non-interference controller 14,with respect to the respective designated combinations of the inputs andthe outputs, based on differences between (i) current values of thecontrol quantities y1, y2, . . . , yn outputted by the control target 20and (ii) target values r1, r2, . . . , rm, using PID control etc. inorder to make current values follow target values.

The non-interference controller 14 is provided in between the feedbackcontroller 13 and the control target 20 and constitutes anon-interference control model 15 along with the control target 20. Thenon-interference controller 14 executes a non-interference control withrespect to each of the designated combinations of the inputs and theoutputs to reduce influence due to mutual interference between thecontrol quantities y1, y2, . . . , yn. Thus, the control target 20receives m inputs u1, u2, . . . , um that have undergone thenon-interference control. Further, the combination of an input and anoutput may be designated based on a designation criteria to give apriority to a combination to provide a maximum gain, for instance.

When such each combination of an input and an output is not designated,the number of possible combinations may reach maximally “m×n” based onthe dependency from respective inputs to respective outputs; thus,interferences between the combinations “m×n” in maximum needconsidering. Further, when the influence of disturbance W to the controltarget 20 is added, it is difficult to realize a non-interferencecontrol actually.

In contrast, under the control system 10 according to the presentembodiment, when m inputs and n outputs of the control target 20 haveone-to-one correspondence (i.e., m=n), n combinations may be designated.Then, non-interference control may be applied to n combinations of theinputs and the outputs; this may reduce greatly the number ofcombinations of the inputs and the outputs, the combinations of whichinterferences need to be considered. In addition, the feedback controlmay be applied to each of n combinations, negating an error between anon-interference control term and the control target 20 to amend amutual interference term automatically. Therefore, the non-interferencecontrol can be realized easily without considering the variation of thecontrol target 40 due to the disturbance W.

In addition, the control system according to the embodiment of thepresent disclosure may be applied to a vehicle steering control system.In the vehicle steering control system, the inputs to a control targetinclude operation quantities such as instruction voltages to actuatorsof an electric power steering, a variable gear transfer steering, and anactive rear steering, for example. In addition, the outputs from thecontrol target include vehicle motion properties of a steering angle(θs), a yaw angle velocity (γ), and a lateral acceleration (ay). In thiscase, the plurality of actuators operate cooperatively with a yaw axisof the vehicle, causing mutual interference, which needs adjustment by askilled technique person. To that end, the control system according tothe embodiment of the present disclosure may be used to the vehiclesteering control system. That is, the non-interference control andfeedback control may be applied to each of the designated combinationsof the inputs and the outputs, thereby achieving easily non-interferencecontrol. This can reduce time or man hours by a skilled person makingtrial-and-error to adjust each of the actuators.

(Vehicle Steering Control System)

The following will explain a vehicle steering control system, which acontrol system according to the embodiment of the present disclosure isapplied to, i.e., which is according to an embodiment of the presentdisclosure, with reference to FIG. 2 to FIG. 13. The vehicle steeringcontrol system includes a steering system as a control target; thesteering system is to assist steering operation of a vehicle, andincludes three systems as follows: EPS (Electric Power Steering); VGTS(Variable Gear Transmission Steering); and ARS (Active Rear Steering).Hereinafter, the systems are referred to, collectively, as anEPS+VGTS+ARS system.

EPS generates a steering assist torque which assists a steering torqueof the steering wheel by the driver. VGTS changes flexibly a turningangle of a front wheel with respect to a turning angle of the steeringwheel, and controls an actual steering angle of the front wheel. To bespecific, the turning angle of the front wheel is set to be large in alow speed and to be small at a high speed. ARS changes flexibly aturning angle of a rear wheel with respect to a turning angle of thesteering wheel, and controls an actual steering angle of the rear wheel.In the present embodiment, the electric motors are used as actuators forthe three respective steering systems. The motors are referred to as anelectric power steering motor, a variable gear transfer steering motor,and an active rear steering motor. In addition, hereinafter, they arereferred to as an EPS motor, a VGTS motor, and an ARS motor.

FIG. 2 illustrates an overall configuration of the EPS+VGTS+ARS system.The EPS+VGTS+ARS system receives a steering torque Ts by manipulation ofthe driver who manipulates the steering wheel 81 as an external inputand turns the front wheels and rear wheels of the vehicle, eventuallychanging the heading direction of the vehicle. When the steering wheel81 is manipulated, a steering shaft 82 rotates. The rotation angle ofthe steering shaft 82 at this time is referred to as a steering angleθs. The bottom end of the steering shaft 82 is connected to a frontoutput axis 85, whereas the front output axis 85 is connected to a frontwheel steering apparatus 86 which has a pinion gear.

Both ends of a front rack 87 are connected with the front wheels 88 viatie rods. When the pinion gear of the front wheel steering apparatus 86rotates by rotation of the front output axis 85, a pair of front wheels98 are steered with an angle responding to the displacement of thestraight-line motion of the front rack 87. The steering angle of thefront wheel 88 at this time is referred to as a front wheel actualsteering angle δf. Both ends of a rear rack 97 are connected with therear wheels 98 via tie rods. When the pinion gear of the rear wheelsteering apparatus 96 rotates by rotation of the rear output axis 95, apair of rear wheels 98 are steered with an angle responding to thedisplacement of the straight-line motion of the rear rack 97. Thesteering angle of the rear wheel 98 at this time is referred to as arear wheel actual steering angle δr.

The EPS motor 50 gives an output torque τa to the front output axis 85via a reduction gear (unshown). The VGTS motor 60 is provided on theaxis of the steering shaft 82, and gives an output torque τg to thefront output axis 85. The rotator angle of the VGTS motor 60 at thistime is referred to as an angle θg, whereas the rotation angle of thefront output axis 85 is referred to as an angle θo. The ARS motor 70gives an output torque τr to the rear output axis 95 connected to therear wheel steering apparatus 96. The rotation angle of the rear outputaxis 95 at this time is referred to as an angle θor. Attention is paidto three vehicle motion properties of the steering angle θs, yaw anglevelocity γ, and lateral acceleration ay with respect to the steeringtorque Ts, in this vehicle steering control system. This is because thethree vehicle motion properties are suitable as a property forevaluating a vehicle manipulation feeling to be mentioned later. The yawangle velocity γ is an angular velocity at which the vehicle rotatesaround the yaw axis z. The lateral acceleration ay is an acceleration atwhich the center axis 90 of the vehicle moves in the lateral directionof the vehicle. The lateral acceleration ay is dependent on a vehiclespeed V, a time differential of a “sideslipping angle β of the vehiclegravity center” which is an angle formed between the heading directionand forth-and-back direction of the vehicle, and a yaw angle velocity γ.

The following will study a control model illustrated in FIG. 3A; thecontrol model includes an EPS+VGTS+ARS system as a control target 40. Tobe specific, the control target 40 includes an EPS motor 50, a VGTSmotor 60, and an ARS motor 70, all of which are actuators for generatingoutputs in the EPS+VGTS+ARS system. The inputs (operation quantities) tothe control target 40 are a VGTS motor voltage Vg, an EPS motor voltageVa, and an ARS motor voltage Vr; the outputs (control quantities) fromthe control target 40 are a steering angle θs, a yaw angle velocity γ,and a lateral acceleration ay. That is, the number of inputs and thenumber of outputs of the control target 40 are three inputs and threeoutputs (3 inputs and 3 outputs).

In this system, the output torques of the EPS motor 50, the VGTS motor60, and the ARS motor 70 operate cooperatively to the yaw axis z; asindicated in FIG. 3A, each of the three inputs operates to the threeoutputs, thereby causing mutual interference. Furthermore, the vehiclereceives the disturbance due to rainstorm, blown fragments, or a roadsurface reactive force depending on the grounding state between tiresand road surfaces; the received disturbance is inputted to the controltarget 40.

The disturbance generally arises in any control system; it is verydifficult to practically detect or presume the disturbance in real time.Therefore, it is difficult to realize theoretically a control whichnegates mutual interference caused by a plurality of inputs and outputsin a control system. To that end, a skilled person needs to maketrial-and-error in tuning of the gain, for instance, to each of theactuators; this requires much time or many man hours.

In contrast, the vehicle steering control system according to thepresent embodiment indicated in FIG. 3B has mainly two features asfollows. The first feature is to designate combinations of inputs andoutputs of a control target 40 in a non-interference control model 35including a non-interference controller 34 in the input side of thecontrol target 40, and provide a non-interference control with respectto each of the designated combinations of inputs and outputs. The secondfeature is to provide a feedback control with respect to each of thedesignated combinations of the inputs and outputs. The two featuresnegate mutual interference, which is caused in between more than oneoutput, as much as possible; the non-interference control can berealized easily without considering the variation of the control target40 due to the disturbance W.

The following will explain a configuration of the embodiment withreference to FIG. 4. A vehicle steering control system 30 of the presentembodiment is indicated by the broken-line block in FIG. 4. The vehiclesteering control system 30 calculates inputs to the control target 40based on the target values which a target value generator 32 generates.Specifically, based on an external input 31 which is a steering torqueTs by a driver, the target value generator 321 generates a steeringangle target value θs^(ref), the target value generator 322 generates ayaw angle velocity target value γ^(ref), the target value generator 323generates a lateral acceleration target value ay^(ref). The targetvalues θs^(ref), γ^(ref), ay^(ref) are then inputted into the vehiclesteering control system 30. The target value generators 321, 322, and323 generate target values θs^(ref), γ^(ref), ay^(ref) with a transferfunction of a secondary delay system to the steering torque Ts, forexample. Thus, the target value generators 321, 322, and 323 arereferred to, collectively, as the target value generator 32.

The vehicle steering control system 30 includes a feedback controller 33and a non-interference controller 34. The feedback controller 33calculates control inputs v1, v2, v3 to the non-interference controller34 by PID control based on differences between the target values and thecurrent values of the control quantities outputted from the controltarget 40 to make the current values follow the target values. In thepresent embodiment, the feedback controller 331 calculates the controlinput v1 from the difference (θs^(ref)−θs) of the steering angle; thefeedback controller 332 calculates the control input v2 from thedifference (γ^(ref)−γ) of the yaw angle velocity γ; and the feedbackcontroller 333 calculates the control input v3 from the difference(ay^(ref)−ay) of the lateral acceleration ay. Thus, the feedbackcontrollers 331, 332, 333 are referred to, collectively, as the feedbackcontroller 33.

The non-interference controller 34 is provided in between the feedbackcontroller 33 and the control target 40, and constitutes thenon-interference control model 35 along with the control target 40. Thedetail of the non-interference control by the non-interference controlmodel 35 will be explained later. The control target 40 includes a VGTSmotor 60, an EPS motor 50, and an ARS motor 70. The control target 40has three inputs and three outputs; namely, three inputs are a VGTSmotor voltage Vg, an EPS motor voltage Va, and an ARS motor voltage Vr,and three outputs are a steering angle θs, a yaw angle velocity γ, and alateral acceleration ay. The current values of the outputted controlquantities θs, γ, and ay are fed back to the feedback controllers 331,332, and 333, respectively. In addition, the disturbance W such as roadsurface reactive force is inputted into the control target 40.

The combinations of the inputs and the outputs are designated optionallyfor three inputs and three outputs. The present embodiment designatesthree combinations to permit the steering angle θs to be controlled bythe VGTS motor voltage Vg, the yaw angle velocity γ to be controlled bythe EPS motor voltage Va, and the lateral acceleration ay to becontrolled by the ARS motor voltage Vr.

The basis of designating the combinations of inputs and outputs is topermit an input to generate an output providing an advantageous effectof the control. To be specific, frequency characteristics of outputsbased on respective inputs are compared to find a combination thatprovides a maximum gain at a noticed specific frequency. Alternatively,a combination may be found which provides a maximum integration value ofa gain in a frequency region from a first frequency to a secondfrequency, i.e., a maximum area in a Bode diagram of the gain.

Reasons for designating combinations according to the present embodimentwill be explained with reference to FIG. 5 to FIG. 7. In FIGS. 5 to 7,for instance, “θs/Vg” indicates a frequency characteristic of an outputθs by an input Vg. With reference to FIG. 5, when the steering angle θsis controlled by the VGTS motor voltage Vg, the gain decline is minimumand the gain is maximum among three in the frequency range of 20 Hz ormore. In contrast, with reference to FIG. 6 and FIG. 7, the control bythe VGTS motor voltage Vg provides the yaw angle velocity γ and thelateral acceleration ay to be minimum among three. Therefore, thecombination of the VGTS motor voltage Vg and the steering angle θs mayprovide an advantageous effect.

Next, with reference to FIG. 6 and FIG. 7, each of the yaw anglevelocity γ and the lateral acceleration ay provides the property by theEPS motor voltage Va and the property by the ARS motor voltage Vr, twoof which are similar, except that an anti-resonance property by the EPSmotor voltage Va is recognized near 8 Hz. However, when seeing FIG. 7 indetail, the control from the ARS motor voltage Vr provides a gain thatexceeds a gain from the control by the EPS motor voltage Va with respectto the lateral acceleration ay near 2 to 3 Hz; thus, the combination ofthe ARS motor voltage Vr and the lateral acceleration ay is designated.Then, the remaining combination of the EPS motor voltage Va and the yawangle velocity γ is designated.

Further, with reference to FIG. 5 to FIG. 7, the frequencycharacteristics of the outputs θs, γ, ay by the inputs Vg, Va, Vrprovide gains to be partially overlapped with each other. In particular,with reference to FIG. 6 and FIG. 7, the frequency characteristics ofthe outputs γ, ay by the inputs Va, Vr provide gains that are almostoverlapped with each other. This indicates that the mutual interferenceoccurs since input/output relation is not of one to one. This poses adifficulty in gain tuning in the design of the controller of each outputθs, γ, ay. To that end, the present embodiment executes anon-interference control for each of the combinations of the inputs andoutputs designated as mentioned above, and a feedback control for eachof the combinations.

The following will explain the non-interference control specifically.

[Derivation of State Space Model]

Expression 1 (1.1, 1.2) provides a general form of an equation of stateabout the control target 40. It is noted that the design of thenon-interference controller neglects “DTs” term of the right side ofExpression 1.1 that is a term concerning the steering torque Ts by thedriver. This is because the number of inputs and the number of outputsneed to be identical for applying the theory of the non-interferencecontrol.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 1} \right\rbrack & \; \\\left\{ \begin{matrix}{\overset{.}{x} = {{Ax} + {Bu} + {DTs}}} \\{y = {Cx}}\end{matrix} \right. & \begin{matrix}(1.1) \\(1.2)\end{matrix}\end{matrix}$

The number of inputs and the number of outputs of the control target 40are 3 inputs and 3 outputs as above-mentioned; thus, the input u isexpressed with a column vector of Expression 2 and the output y isexpressed with a column vector of Expression 3.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 2} \right\rbrack & \; \\{u = {\begin{bmatrix}u_{1} \\u_{2} \\u_{3}\end{bmatrix} = \begin{bmatrix}V_{g} \\V_{a} \\V_{r}\end{bmatrix}}} & (2) \\\left\lbrack {{Expression}\mspace{14mu} 3} \right\rbrack & \; \\{y = \begin{bmatrix}\theta_{s} \\\gamma \\a_{y}\end{bmatrix}} & (3)\end{matrix}$

With respect to the state variable x, the EPS+VGTS+ARS system is dividedinto (i) the EPS+VGTS system for the front wheel, and (ii) the ARSsystem for the rear wheel, and the equation of motion between eachsteering motor and a rotation load is analyzed; this extracts variableswhich affects the output. The detailed explanation of the equation ofmotion is omitted. As a result of the analysis, the state variablevector x is expressed by a combination vector of 15 elements whichcombines “a state vector xp of six elements”, “a state vector of timedifferentials of six elements of the state vector xp”, and “a statevector i of three elements relating to motor current”.

The state vector xp, which is a partial vector of the state variablevector x, and its time differential are indicated as Expression 4.1 andExpression 4.2. The elements of the state vector xp are as follows.

θs: Steering wheel angle

θg: VGTS motor rotor angle

θo: Rotation angle of front output axis 85

ηor: Rotation angle of rear output axis 95

β: Sideslipping angle of vehicle gravity center

γ: Yaw angle velocity

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 4} \right\rbrack & \; \\{x_{p} = \begin{bmatrix}\theta_{s} \\\theta_{g} \\\theta_{o} \\\theta_{or} \\\beta \\\gamma\end{bmatrix}} & (4.1) \\{{\overset{.}{x}}_{p} = \begin{bmatrix}{\overset{.}{\theta}}_{s} \\{\overset{.}{\theta}}_{g} \\{\overset{.}{\theta}}_{o} \\{\overset{.}{\theta}}_{or} \\\overset{.}{\beta} \\\overset{.}{\gamma}\end{bmatrix}} & (4.2)\end{matrix}$

In addition, the state vector i concerning motor current is indicated asExpression 5. The elements of the state vector i are as follows.

ig: VGTS motor current

ia: EPS motor current

ir: ARS motor current

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 5} \right\rbrack & \; \\{i = \begin{bmatrix}i_{g} \\i_{a} \\i_{r}\end{bmatrix}} & (5)\end{matrix}$

The state variable vector xp is indicated as Expression 6.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 6} \right\rbrack & \; \\{x = \begin{bmatrix}x_{p} \\{\overset{.}{x}}_{p} \\i\end{bmatrix}} & (6)\end{matrix}$

Expressions 1.1 and 1.2 are replaced by Expressions 7.1 and 7.2 fromExpressions 2 to 6. DTs term is disregarded in Expression 7.1;Expression 7.1 does not include DTs.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 7} \right\rbrack & \; \\\left\{ \begin{matrix}{\begin{bmatrix}{\overset{.}{x}}_{p} \\{\overset{..}{x}}_{p} \\\overset{.}{i}\end{bmatrix} = {{A\begin{bmatrix}x_{p} \\{\overset{.}{x}}_{p} \\i\end{bmatrix}} + {B\begin{bmatrix}V_{g} \\V_{a} \\V_{r}\end{bmatrix}}}} \\{\begin{bmatrix}\theta_{s} \\\gamma \\a_{y}\end{bmatrix} = {C\begin{bmatrix}x_{p} \\{\overset{.}{x}}_{p} \\i\end{bmatrix}}}\end{matrix} \right. & \begin{matrix}(7.1) \\\; \\\; \\\; \\(7.2)\end{matrix}\end{matrix}$

Each of a matrix A and a matrix B, which consists of constant elements,is explained briefly. The matrix A includes constants with respect toelements concerning secondary differential of vector xp, such as amoment of inertia of a motor and a rotation load, a torque constant, aviscous friction coefficient of a component member, and a speedreduction ratio. In addition, the matrix A includes constants withrespect to elements concerning time differential of the vector i, suchas a reactance and resistance of each motor. The matrix B includesconstants with respect to elements concerning time differential of thevector i, such as a reactance and resistance of each motor.

In contrast, a matrix C of an output equation has three rows and fifteencolumns as indicated as Expression 8.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 8} \right\rbrack & \; \\{C = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & \left. 0 \right| & 0 & 0 & 0 & 0 & 0 & \left. 0 \right| & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & \left. 1 \right| & 0 & 0 & 0 & 0 & 0 & \left. 0 \right| & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & \left. V \right| & 0 & 0 & 0 & 0 & V & \left. 0 \right| & 0 & 0 & 0\end{bmatrix}} & (8)\end{matrix}$

The third row vector of the matrix C reflects Expression 9 about alateral acceleration ay. In Expression 9, V is a vehicle speed.

[Expression 9]

α_(y) =V({dot over (β)}+γ)   (9)

[Design of Non-Interference Controller]

Now, state feedback is applied to the non-interference control model 35in FIG. 3B and FIG. 4 with Expression 10.

[Expression 10]

u=Fx+G ν  (10)

Here, v is a control input to the non-interference controller 34, andconsists of three elements (v1, v2, v3). In contrast, u is an output ofthe non-interference controller 34, and an input to the control target40 while consisting of three elements (Vg, Va, Vr). G is a gain from vto u, and F is a state feedback gain in the non-interference controller34. The non-interference controller 34 is designed, with respect to therelation between the control inputs v1, v2, v3, and outputs θs, γ, ay ofthe control target 40, such that v1 affects only θs, v2 affects only γ,and v3 affects only ay.

Expression 10 is assigned to Expression 1.1; this obtains Expression 11which is an equation of state after non-interference. It is noted that,as mentioned above, DTs term is disregarded and is not described.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 11} \right\rbrack & \; \\\begin{matrix}{\overset{.}{x} = {{Ax} + {Bu}}} \\{= {{Ax} + {B\left( {{Fx} + {G\; v}} \right)}}} \\{= {{\left( {A + {BF}} \right)x} + {{BG}\; v}}}\end{matrix} & (11)\end{matrix}$

When Expression 11 and Expression 1.2 are subjected to Laplacetransform, a transfer function H_(FG) after the non-interference isindicated with Expression 12.1. In addition, since the number of inputsis three (m=3), the transfer function H_(FG)(s) is indicated with amatrix with three rows and three columns as indicated in Expression12.2. This matrix is a diagonal matrix, in which the element of the rowi and the column j is (i) zero when i≠j, and (ii) an inverse number ofσ-order polynomial of Laplace transform s when i=j. In addition,regarding the order σ of s, σ1=3 at a polynomial with the first row andthe first column; σ2=4 at a polynomial with the second row and thesecond column; and σ3=3 at a polynomial with the third row and the thirdcolumn. The explanation about the derivation is omitted.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 12} \right\rbrack & \; \\{{H_{FG}(s)} = {{C\left( {{sI} - A - {BF}} \right)}^{- 1}{BG}}} & (12.1) \\{= \begin{bmatrix}\frac{1}{s^{3} + {\alpha_{11}s^{2}} + {\alpha_{12}s} + \alpha_{13}} & 0 & 0 \\0 & \frac{1}{s^{4} + {\alpha_{21}s^{3}} + {\alpha_{22}s^{2}} + {\alpha_{23}s} + \alpha_{24}} & 0 \\0 & 0 & \frac{1}{s^{3} + {\alpha_{31}s^{2}} + {\alpha_{32}s} + \alpha_{33}}\end{bmatrix}} & (12.2)\end{matrix}$

In order to apply non-interference control to the non-interferencecontrol model 35, the gain G and the status feedback gain F only need tobe designated as Expression 13.1 and Expression 13.2, respectively.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 13} \right\rbrack & \; \\\left\{ \begin{matrix}{G = B^{*{- 1}}} \\{F = {- {G\begin{bmatrix}{{c_{1}^{T}A^{3}} + {\alpha_{11}c_{1}^{T}A^{2}} + {\alpha_{12}c_{1}^{T}A} + {\alpha_{13}c_{1}^{T}}} \\{{c_{2}^{T}A^{4}} + {\alpha_{21}c_{2}^{T}A^{3}} + {\alpha_{22}c_{2}^{T}A^{2}} + {\alpha_{23}c_{2}^{T}A} + {\alpha_{24}c_{2}^{T}}} \\{{c_{3}^{T}A^{3}} + {\alpha_{31}c_{3}^{T}A^{2}} + {\alpha_{32}c_{3}^{T}A} + {\alpha_{33}c_{3}^{T}}}\end{bmatrix}}}}\end{matrix} \right. & \begin{matrix}(13.1) \\\; \\(13.2)\end{matrix}\end{matrix}$

ci^(T)(i=1, 2, 3) is equivalent to the i-th row vector of the matrix C(Expression 8), and is indicated with Expression 14.1 to 14.3.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 14} \right\rbrack & \; \\\left\{ \begin{matrix}{c_{1}^{T} = \begin{bmatrix}1 & 0 & 0 & 0 & 0 & \left. 0 \right| & 0 & 0 & 0 & 0 & 0 & \left. 0 \right| & 0 & 0 & 0\end{bmatrix}} & (14.1) \\{c_{2}^{T} = \begin{bmatrix}0 & 0 & 0 & 0 & 0 & \left. 1 \right| & 0 & 0 & 0 & 0 & 0 & \left. 0 \right| & 0 & 0 & 0\end{bmatrix}} & (14.2) \\{c_{3}^{T} = \begin{bmatrix}0 & 0 & 0 & 0 & 0 & \left. V \right| & 0 & 0 & 0 & 0 & V & \left. 0 \right| & 0 & 0 & 0\end{bmatrix}} & (14.3)\end{matrix} \right. & \;\end{matrix}$

Expression 13.1 indicates that G is an inverse matrix of adjoint matrix(conjugate transposed matrix) B* of B. It is premised to obtain G thatan inverse matrix exists in B* and B* is regular. Although thecalculation is omitted, in the present embodiment, it is confirmed thatB* is regular.

The following designs coefficients α₁₁ to α₃₃ of the denominatorpolynomials of Expression 13.2. It is supposed that the poles of threedenominator polynomials are (−pk1), (−pk2), and (−pk3); Expression 12.2is rewritten into Expression 15. Now, the transfer function H_(FG)(s)after non-interference is obtained; a suitable frequency is applied to(−pk1), (−pk2), and (−pk3), to verify the non-interference using thetransfer function H_(FG)(s).

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 15} \right\rbrack & \; \\{{H_{FG}(s)} = \begin{bmatrix}\frac{1}{\left( {s + {p\; k_{1}}} \right)^{3}} & 0 & 0 \\0 & \frac{1}{\left( {s + {p\; k_{2}}} \right)^{4}} & 0 \\0 & 0 & \frac{1}{\left( {s + {p\; k_{3}}} \right)^{3}}\end{bmatrix}} & (15)\end{matrix}$

The non-interference control model 35, which the above-mentionednon-interference control is applied to, provides frequencycharacteristics from the control inputs v1, v2, v3 to the outputs θs, γ,ay, as indicated in FIG. 8 to FIG. 10, wherein “θs/v1” indicates afrequency characteristic of the output θs by the control input v1. FIG.8 indicates that the gain by the control input v1 is high over the wholeof frequencies, with respect to the steering angle θs. FIG. 9 indicatesthat the gain by the control input v2 is high over the whole offrequencies, with respect to the yaw angle velocity γ. FIG. 10 indicatesthat the gain by the control input v3 is high over the whole offrequencies, with respect to the lateral acceleration ay. This provesthat non-interference is achieved.

As mentioned above, the vehicle steering control system 30 according tothe present embodiment applies non-interference control to each ofdesignated combinations of the inputs and outputs, thereby permittingthe control inputs v1, v2, v3 of the non-interference controller 34 toaffect the outputs θs, γ, ay, respectively. That is, the control inputv1 is permitted to affect only the output θs; the control input v2 ispermitted to affect only the output γ; and the control input v3 ispermitted to affect only the output ay. This facilitates the independentcontrol of each of three vehicle motion properties of the steering angleθs, the yaw angle velocity γ, and the lateral acceleration ay, withrespect to the steering torque Ts. In addition, the feedback control maybe applied to each of the designated combinations; this negates an errorbetween the non-interference control term and the control target 40 toamend a mutual interference term automatically. Therefore, thenon-interference control can be realized easily without considering thevariation of the control target 40 due to the disturbance W.

Thus, the vehicle steering control system 30 according to the presentembodiment may control independently each of three vehicle motionproperties of the steering angle θs, the yaw angle velocity γ, and thelateral acceleration ay, with respect to the steering torque Ts. Thefollowing will explain an operation feeling evaluation of the vehicleusing the above advantageous effect.

In the target value generators 321, 322, 323 in FIG. 4, target valuesθs^(ref), γ^(ref), ay^(ref) of the steering angle, yaw angle velocity,and lateral acceleration with respect to the steering torque Is aregenerated by using the transfer function (Expression 16) of thesecondary delay system to the steering torque Ts, for instance. InExpression 16, K represents a proportionality coefficient; ω_(n)represents a natural angular frequency; and ζ represents an attenuationcoefficient.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 16} \right\rbrack & \; \\{{G(s)}^{ref} = \frac{K\; \omega_{n}^{2}}{s^{2} + {2\; {\zeta\omega}_{n}s} + \omega_{n}^{2}}} & (16)\end{matrix}$

The use of the transfer function of the secondary delay system permitsconvergence values of the step response waveforms to come to targetvalues θs^(ref, γ) ^(ref), ay^(ref). In addition, the overshooting Os(%) and the excessive time Tp can be calculated with Expressions 17, 18.

$\begin{matrix}\left\lbrack {{Expression}\mspace{14mu} 17} \right\rbrack & \; \\{O_{s} = {100\; ^{\frac{{- \zeta}\; \pi}{\sqrt{1 - \zeta^{2}}}}}} & (17) \\\left\lbrack {{Expression}\mspace{14mu} 18} \right\rbrack & \; \\{T_{p} = \frac{\pi}{\omega_{n}\sqrt{1 - \zeta^{2}}}} & (18)\end{matrix}$

The coefficients K, ω_(n), ζ of the transfer function in Expressions 16to 18 are estimated as follows. The waveforms of θs, γ, ay, which areobtained by simulating the coefficients K, ω_(n), ζ, are subjected tothe curve fitting against the respective step response waveforms ofproperties θs, γ, ay in a base vehicle as a standard. FIG. 11 to FIG. 13illustrate the step response waveforms of θs, γ, ay which are obtainedas explained above, and the following properties of the outputs θs, γ,ay obtained using the non-interference controller 34. The target valueand the line of the following property of the output overlap with eachother on the waveform with respect to each of the steering angle θs inFIG. 11, the yaw angle velocity γ in FIG. 12, and the lateralacceleration ay in FIG. 13; this proves that the outputs follow well thetarget values θs^(ref), γ^(ref), ay^(ref), respectively.

Generally the step response waveform is suitable for evaluation of atransient characteristic of a system. Thus, in evaluating an operationfeeling at the time of manipulating the steering wheel, the attenuationcharacteristic or response characteristic of the step response waveformis evaluated; thereby, the driver's sensibility of manipulating thesteering wheel repeatedly in the state changing every moment can beevaluated quantitatively. To be specific, the present embodiment changesindependently the overshooting Os and the excessive time Tp of the stepresponse waveform; this changes the vehicle motion property easily andconfirms the influence on operation feeling. This achieves aquantitative evaluation of the operation feeling easily as compared witha conventional evaluation using Lissajous waveform.

Other Embodiments

(a) Combinations of the inputs and outputs designated in the vehiclesteering control system 30 may not be limited to the combinations of“VGTS motor voltage Vg and steering angle θ”, “EPS motor voltage Va andyaw angle velocity γ”, and “ARS motor voltage Vr and lateralacceleration ay” that were adopted in the above embodiment. For example,the frequency characteristics of the output of the yaw angle velocity γto the inputs of the EPS motor voltage Va and the ARS motor voltage Vrdo not provide a significant difference between them (refer to FIG. 6).Further, the frequency characteristics of the output of the lateralacceleration ay to the inputs of the EPS motor voltage Va and the ARSmotor voltage Vr do not provide a significant difference between them(refer to FIG. 7). Thus, the combinations of “EPS motor voltage Va andlateral acceleration ay”, and “ARS motor voltage Vr and the yaw anglevelocity γ” may be designated alternatively.

(b) The actuators to generate the outputs in the EPS+VGTS+ARS system maybe not limited to the electric motors but be other actuators to outputrotation power or linear power.

(c) The control system according to the present disclosure may not belimited to the vehicle steering control system but be any control systemwhich controls any physical quantity such as temperature, pressure,position. In addition, the number m of the inputs and the number n ofthe outputs of the control target may not be limited to m=n=3 but be m=n(≧2) when the mutual interference may occur between n outputs.

(d) Furthermore, even when the number m of the inputs and the number nof the outputs of the control target are m≠n, the control systemaccording to the present disclosure may be applicable. For example, thetechnique of the the present disclosure may be applied to the case thatthe number of the inputs is different from the number of the outputs byusing the technique described in the following reference document.

(Reference Document)

“The multi-stage non-interference method by series parallel connectionof predistorters”, Assignment number 14550455, Grants-in-aid forscientific research in the fiscal years of Heisei 14 (2002) and Heisei15 (2003), (Basic research (C), (2)), Result of research report,published in December Heisei 16 (2004)

FIG. 14 indicates an example where the number m of inputs and the numbern of outputs of a control target 21 are two and three, i.e., “m<n.” InFIG. 14 and FIG. 15, a substantively identical element or configurationis assigned with an identical reference number; the duplicatedexplanation is omitted. FIG. 14 indicates a non-interference controlmodel 18 that includes an input expander 16 of “multi inputs and 1output” in between a non-interference controller 14 and a control target21. two inputs u1, u2 among the inputs u1, u2, u3 having undergone thenon-interference control by the non-interference controller 14 areadopted in an alternative way by the input expander 16 depending on afrequency range to be integrated into one input u1′. To be specific,when the input u1 passes through a highpass filter 161, the lowfrequency band lower than the cutoff frequency is cut; when the input u2passes through a lowpass filter 162, the high frequency band higher thanthe cutoff frequency is cut. The input u3 is inputted into the controltarget 21 as it is. The control target 21 outputs three outputs y1, y2,y3 based on the two inputs u1′ and u3.

Thus, the configuration where the number m of the inputs and the numberm of the outputs of the control target 21 have a relation of “m<n” issupposed to provide a type different from that of “m=n”. However, inanother view, an “expansion unit” may be provided by integrating theinput expander 16 and the control target 21. This expansion unitprovides the number m* of inputs and the number n of the outputs to bethree and three, respectively. Therefore, according to this view, theconfiguration in FIG. 14 may be a type to provide an expansion unit atthe output side of the non-interference controller 14, the expansionunit being with the numbers m*, n of the inputs and outputs being m*=n,by replacing the control target with m=n.

(e) In addition, FIG. 15 indicates a non-interference control model 19where the numbers m, n of the inputs and the outputs of a control target22 are four and three, respectively, namely “m>n.” In addition, an inputexpander 17 with one input and multiple outputs is provided in betweenthe non-interference controller 14 and the control target 22. The inputu1 is divided into two by the input expander 17. One is inputted intothe control target 22 as an input u1 a via a controller 171; the otheris inputted into the control target 22 as an input u1 b via a controller172. Inputs u2, u3 are inputted into the control target 22 as they are.The control target 22 outputs three outputs y1, y2, y3 based on the fourinputs u1 a, u1 b, u2, u3.

This configuration may be considered, like that of (d), as a typedifferent from the control target with the numbers of the inputs and theoutputs having a relation of m=n. Alternatively, one expansion unit withthe numbers m*, n of the inputs and outputs having a relation of “m*=n.”

While the present disclosure has been described with reference topreferred embodiments thereof, it is to be understood that thedisclosure is not limited to the preferred embodiments andconstructions. The present disclosure is intended to cover variousmodification and equivalent arrangements. In addition, while the variouscombinations and configurations, which are preferred, other combinationsand configurations, including more, less or only a single element, arealso within the spirit and scope of the present disclosure.

What is claimed is:
 1. A control system that controls a control targetthat provides a plurality of n outputs of control quantities based on aplurality of m inputs of operation quantities, wherein m=n and each of mand n is a natural number that is more than one, the control systemcomprising: a plurality of feedback controllers, each of whichcalculates the operation quantity based on a difference between (i) atarget value, which is generated by a target value generator, the targetvalue corresponding to the control quantity and, and (ii) a currentvalue of the output provided by the control target; and anon-interference controller provided between (i) the plurality offeedback controllers and (ii) the control target, the non-interferencecontroller executing a non-interference control to reduce influence dueto mutual interference between the outputs provided by the controltarget, wherein: combinations of the inputs and the outputs in thecontrol target are designated; and the non-interference control by thenon-interference controller and the feedback control by the feedbackcontrollers are executed with respect to each of the designatedcombinations of the inputs and the outputs.
 2. The control systemaccording to claim 1, wherein: when designating the combinations of theinputs and the outputs in the control target, a priority is given to asubject combination of (i) an input among the plurality of inputs and(ii) an output among the plurality of outputs, the subject combinationproviding a maximum gain.
 3. The control system according to claim 1,wherein: each combination is of (i) one input among the plurality ofinputs and (ii) one output among the plurality of outputs; and a numberof the designated combinations is equal to n being a number of theoutputs, n being equal to m being a number of the inputs.
 4. A vehiclesteering control system to which the control system according to claim 1is applied, the vehicle steering control system controlling steering ofa vehicle while providing, as the outputs of the control target, atleast two control quantities among three control quantities that are (i)a steering angle, (ii) a yaw angle velocity, and (iii) a lateralacceleration, the three control quantities being vehicle propertiesgenerated based on a driver's steering torque.
 5. The vehicle steeringcontrol system according to claim 4, wherein: the control targetincludes a variable gear transfer steering motor which controls anactual steering angle of a front wheel; and the designated combinationis of (i) a motor voltage of the variable gear transfer steering motorthat serves as an input and (ii) a steering angle of the vehicle thatserves as an output.
 6. The vehicle steering control system according toclaim 4, wherein: the control target includes an electric power steeringmotor which assists a steering force by a driver; and the designatedcombination is of (i) a motor voltage of the electric power steeringmotor that serves as an input and (ii) a yaw angle velocity of thevehicle that serves as an output.
 7. The vehicle steering control systemaccording to claim 4, wherein: the control target includes an activerear steering motor which controls an actual steering angle of a rearwheel; and the designated combination is of (i) a motor voltage of theactive rear steering motor that serves as an input and (ii) a lateralacceleration of the vehicle that serves as an output.